Generating Multiple Spherical Attractors via Parameter Switching Control

A three-dimensional smooth continuous-time system with a parameter and two quadratic terms is constructed and a spherical attractor is generated. There exist multiple coexisting spherical attractors based on offset boosting. Two classes of switching signals that depend on the time and the state are designed respectively. By employing a parameter switching control technique, multiple spherical attractors can be generated. Simultaneously, complex chaotic attractors can also be generated by designing a state-dependent switching signal. Numerical examples and corresponding simulations show the effectiveness of the switching control technique.

Additive Mixed Sensitivity Design of PID Controllers for Continuous-Time System with Uncertain Time-Delay

This paper presents an algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers in an integral-derivative plane that stabilizes and satisfies additive mixed sensitivity constraint with an uncertain time delay for a continuous-time system. This algorithm solves the singularity problem of designing PID controllers in the integral and derivative plane and estimates achievable ranges of proportional gain of the PID controllers. A numerical cascaded ball and beam with unity feedback control of an SRV-DC motor and uncertain communication time delays in the system process demonstrate the application of this methodology. In this application, the additive weight bounds the additive errors for the cascaded ball and beam and the closed-loop SRV-DC motor system transfer function with the internal communication time delays

Event-triggered control for a linear continuous-time system under resource constraint environment

<div>A network-based event-triggered control is proposed for the continuous linear system. The primary feature of the proposed event-triggered control is to broadcast the current measurements when a pre-defined condition on input error is satisfied, which can avoid the redundant control updates from the controller to the actuator. Secondly, it provides an augmented system performance by appropriate selection of design parameters. Moreover, a dynamic threshold is introduced in the triggered condition to further improve the trade-off between resource utilization and system performance.</div>

Event-triggered control for a linear continuous-time system under resource constraint environment

<div>A network-based event-triggered control is proposed for the continuous linear system. The primary feature of the proposed event-triggered control is to broadcast the current measurements when a pre-defined condition on input error is satisfied, which can avoid the redundant control updates from the controller to the actuator. Secondly, it provides an augmented system performance by appropriate selection of design parameters. Moreover, a dynamic threshold is introduced in the triggered condition to further improve the trade-off between resource utilization and system performance.</div>

Invariance under discretization for positive systems

Positive dynamical or control systems have all their variables nonnegative. Euler discretization transforms a continuous-time system into a system on a discrete time scale. Some structural properties of the system may be preserved by discretization, while other may be lost. Four fundamental properties of positive systems are studied in the context of discretization: positivity, positive stability, positive reachability and positive observability. Both linear and nonlinear systems are investigated.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.